Computational Information Geometry Wonderland

Legendre-Fenchel duality is at the heart of dually flat spaces in information geometry. Convex functions come in pairs, called convex conjugates. The basic principle is that if you plot the epigraph of the function F and reinterpret it at the intersection of support halfspaces, you get the dual geometric representation of the epigraph. You can parameterize this dual representation using the convex conjugate function. Thus the Legendre-Fenchel transformation is sometimes called the slope transform.

More details in the memo:
NoteLegendreTransformation.pdf

++x-x,
Frank.